Showing papers in "Boletin De La Sociedad Matematica Mexicana in 2022"

On coefficient problems for functions starlike with respect to symmetric points

Abstract: Abstract The main idea of the study on coefficient problems in various classes of analytic functions (univalent or nonunivalent) is to express the coefficients of functions in a given class by the coefficients of corresponding functions with positive real part. Thus, coefficient functionals can be studied using inequalities known for the class $${\mathcal {P}}$$ P . Lemmas obtained by Libera and Złotkiewicz and by Prokhorov and Szynal play a special role in this approach. Recently, a new way leading to results on coefficient functionals has been pointed out. This approach is based on relating the coefficients of functions in a given class and the coefficients of corresponding Schwarz functions. In many cases, if we follow this approach, it is easy to predict the exact estimate of the functional and make the appropriate computations. In the proofs of these estimates are used not only classical results (the Schwarz–Pick Lemma or Wiener’s inequality), but also inequalities obtained either recently (e.g. by Efraimidis) or long ago yet almost forgotten (Carlson’s inequality). In this paper, a number of coefficient problems will be solved using the new approach described above. The object of our study is the class of starlike functions with respect to symmetric points associated with the exponential function.

On coefficient problems for functions starlike with respect to symmetric points

Abstract: Abstract The main idea of the study on coefficient problems in various classes of analytic functions (univalent or nonunivalent) is to express the coefficients of functions in a given class by the coefficients of corresponding functions with positive real part. Thus, coefficient functionals can be studied using inequalities known for the class $${\mathcal {P}}$$ P . Lemmas obtained by Libera and Złotkiewicz and by Prokhorov and Szynal play a special role in this approach. Recently, a new way leading to results on coefficient functionals has been pointed out. This approach is based on relating the coefficients of functions in a given class and the coefficients of corresponding Schwarz functions. In many cases, if we follow this approach, it is easy to predict the exact estimate of the functional and make the appropriate computations. In the proofs of these estimates are used not only classical results (the Schwarz–Pick Lemma or Wiener’s inequality), but also inequalities obtained either recently (e.g. by Efraimidis) or long ago yet almost forgotten (Carlson’s inequality). In this paper, a number of coefficient problems will be solved using the new approach described above. The object of our study is the class of starlike functions with respect to symmetric points associated with the exponential function.

Inverse problem for a differential operator on a star-shaped graph with nonlocal matching condition

Abstract: In this paper, we develop two approaches to investigation of inverse spectral problems for a new class of nonlocal operators on metric graphs. The Laplace differential operator is considered on a star-shaped graph with nonlocal integral matching condition. This operator is adjoint to the functional-differential operator with frozen argument at the central vertex of the graph. We study the inverse problem that consists in the recovery of the integral condition coefficients from the eigenvalues. We obtain the spectrum characterization, reconstruction algorithms, and prove the uniqueness of the inverse problem solution.

Approximating common fixed points of a family of non-self mappings in CAT(0) spaces

Abstract: In this paper, we construct an iterative scheme for approximating common fixed points of a countable family of quasi-nonexpansive non-self mappings in a complete CAT(0) space. In addition, we prove $$\triangle $$ -convergence and strong convergence results of the scheme under appropriate conditions. Moreover, we construct an iterative scheme for approximating common fixed points of a countable family of demicontractive mappings and establish strong convergence result of the scheme under some mild conditions. Our results improve and generalize most of the results in the literature.

Sums of Fibonacci numbers close to a power of 2

Abstract: In this paper, we find all sums of two Fibonacci numbers which are close to a power of 2. As a corollary, we also determine all Lucas numbers close to a power of 2. The main tools used in this work are lower bounds for linear forms in logarithms due to Matveev and Dujella–Pethö version of the Baker–Davenport reduction method in diophantine approximation. This paper continues and extends the previous work of Chern and Cui.

Stewart’s theorem revisited: suppressing the norm $$\pm 1$$ hypothesis

Abstract: Let \(\gamma\) be an algebraic number of degree 2 and not a root of unity. In this note we show that there exists a prime ideal \({\mathfrak {p}}\) of \({\mathbb {Q}}(\gamma )\) satisfying \( u _{\mathfrak {p}}(\gamma ^n-1)\ge 1\), such that the rational prime p underlying \({\mathfrak {p}}\) grows quicker than n.

Some missed congruences modulo powers of 2 for t-colored overpartitions

Abstract: Recently, Nayaka and Naika (2022) proved several congruences modulo $16$ and $32$ for $t$-colored overpartitions with $t=5,7,11$ and $13$. We extend their list using an algorithmic technique.